Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit Comparison Test

  1. Jan 9, 2015 #1
    In my textbook it says if you are comparing limn->infinity of an/bn an>0 and bn>0 for the limit comparison test to apply.

    It says nothing about "an" having to be greater than "bn", so as long as both are positive for each term I can use the limit comparison test right? It isn't like the direct comparison test where you need to worry about having all of a sequence's terms be larger/smaller than the one you are comparing to?

    Thanks
     
  2. jcsd
  3. Jan 9, 2015 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    If an/bn -> 0, you know very little about bn if you are using an as a comparison.
     
  4. Jan 12, 2015 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Right. The limit comparison test tells you if the two sequences have the same sort of behavior when n gets large. You don't need one sequence to be greater than or less than the other to see if they behave similarly for large n.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook